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sage:from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5850, base_ring=CyclotomicField(60))
M = H._module
chi = DirichletCharacter(H, M([50,9,20]))
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pari:[g,chi] = znchar(Mod(5333,5850))
\(\chi_{5850}(653,\cdot)\)
\(\chi_{5850}(887,\cdot)\)
\(\chi_{5850}(1127,\cdot)\)
\(\chi_{5850}(1823,\cdot)\)
\(\chi_{5850}(2063,\cdot)\)
\(\chi_{5850}(2297,\cdot)\)
\(\chi_{5850}(3227,\cdot)\)
\(\chi_{5850}(3233,\cdot)\)
\(\chi_{5850}(3467,\cdot)\)
\(\chi_{5850}(4163,\cdot)\)
\(\chi_{5850}(4397,\cdot)\)
\(\chi_{5850}(4403,\cdot)\)
\(\chi_{5850}(4637,\cdot)\)
\(\chi_{5850}(5333,\cdot)\)
\(\chi_{5850}(5567,\cdot)\)
\(\chi_{5850}(5573,\cdot)\)
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sage:chi.galois_orbit()
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pari:order = charorder(g,chi)
[ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\((3251,3277,2251)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{3}{20}\right),e\left(\frac{1}{3}\right))\)
| \(a\) |
\(-1\) | \(1\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \( \chi_{ 5850 }(5333, a) \) |
\(1\) | \(1\) | \(-i\) | \(e\left(\frac{17}{30}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{7}{15}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(i\) |
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sage:chi.jacobi_sum(n)
